Binary mass transfer in 3D: Mass Transfer Rate and Morphology
Mass transfer is crucial in binary evolution, yet its theoretical treatment has long relied on analytic models whose key assumptions remain debated. We present a direct and systematic evaluation of these assumptions using high-resolution 3D hydrodynamical simulations including the Coriolis force. We simulate streams overflowing from both the inner and outer Lagrangian points, quantify mass transfer rates, and compare them with analytic solutions. We introduce scaling factors, including the overfilling factor, to render the problem dimensionless. The donor-star models are simplified, with either an isentropic initial stratification and adiabatic evolution or an isothermal structure and evolution, but the scalability of this formulation allows us to extend the results for a mass-transferring system to arbitrarily small overfilling factors for the adiabatic case. We find that the Coriolis force -- often neglected in analytic models -- strongly impacts the stream morphology: breaking axial symmetry, reducing the stream cross section, and shifting its origin toward the donor's trailing side. Contrary to common assumptions, the sonic surface is not flat and does not always intersect the Lagrangian point: instead, it is concave and shifted, particularly toward the accretor's trailing side. Despite these structural asymmetries, mass transfer rates are only mildly suppressed relative to analytic predictions and the deviation is remarkably small -- within a factor of two (ten) for the inner (outer) Lagrangian point over seven orders of magnitude in mass ratio. We use our results to extend the widely-used mass-transfer rate prescriptions by Ritter(1988) and Kolb&Ritter(1990), for both the inner and outer Lagrangian points. These extensions can be readily adopted in stellar evolution codes like MESA, with minimal changes where the original models are already in use.